Sinusoidal electric fields, nonlinear

Figure 4.20 A sinusoidal electric field of angular frequency u> in a second-order nonlinear optical medium creates a polarization with component at 2tn( second-harmonic) and a steady (dc) component...

A simple thin film technique has been developed to measure the electrical properties of polyelectrolyte solutions under sinusoidal electric fields of 100-500 v/cm at frequencies of. 10-10 KHz. Ohmic heating is largely avoided by the rapid transfer of heat to the electrodes and by the high surface to volume ratios. The resulting temperature is not sufficient to damage the medium. Current and voltage wave forms are monitored directly so that dispersion and nonlinear phenomena of the medium can be viewed directly as functions of frequency, voltage, and concentration of the solution. Possible mechanisms for the observed phenomena are discussed. 

When a polymer is subject to an intense sinusoidal electric field such as that due to an intense laser pulse, Fourier analysis of the polarization response can be shown to contain not only terms in the original frequency co, but also terms in 2(0 and 3nonlinear response depends on the square of the intensity of the incident beam for 2co, and the third power for 3 . For the second-order effects, the system must have some asymmetry, as discussed previously. For poling, this means both high voltage and a chemical organization that will retain the resulting polarization for extended periods of time. Polymeric systems investigated have been of three basic types ... 

The FEBS technique utihzes the electric and optical anisotropies of molecules dissolved in the solution. When the external electric field is applied to a solution containing molecules with the anisotropic polarizability, the molecules tend to be oriented in the direction of the applied electric field. If moreover the molecules have the optical anisotropy, the solution exhibits the birefringence, which is called the Kerr effect [171] as a nonlinear optical effect. In the FEBS, where the sinusoidal electric field is applied, the Kerr constants are measured by varying the frequency/ of the sinusoidal wave. In this sense, the FEBS closely resembles the dielectric relaxation spectroscopy [172]. 

Figure Bl.5.2 Nonlinear dependence of tire polarization P on the electric field E. (a) For small sinusoidal input fields, P depends linearly on hence its hannonic content is mainly tiiat of E. (b) For a stronger driving electric field E, the polarization wavefomi becomes distorted, giving rise to new hannonic components. The second-hamionic and DC components are shown.

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